A weak contractive condition and some fixed point theorems

Abstract

Fixed point theorems for weak-(ψ,α, β)- contractive mappings have been introduced and investigated for different kinds of metric spaces. The paper first discusses a particular condition and then a weak contractive condition generalizing existing such conditions is defined. Our primary aim is to investigate the Banach, Kannan and Chatterjea’s fixed point theorems in complete metric spaces satisfying the new weak contractive condition and their applications. In the sequel, several auxiliary results are investigated and also incorporated sufficient number of examples in suitable places to justify certain claims.